N. Vlassis and A. Likas. A kurtosis-based dynamic approach to gaussian mixture modeling. IEEE Trans. Systems, Man, and Cybernetics, Part A, 29:393--399, 1999.  Home/Search   Document Details and Download   Summary   Related Articles   Check

.... therein) and in non destructive evaluation of materials [4] Among others, a popular estimation approach relies on the finite kernel mixture model (MOK) which tries to approximate a probability density function by means of an adjustable superposition of flexible kernels (for a review see [18]) This method is very interesting in a neural network viewpoint because it may be directly implemented by means of network topologies like the classical multilayer perceptron and the probabilistic neural network [1, 9, 17] However, when the samples of the random process under observation are ....

N.A. Vlassis and A. Likas, A Kurtosis-Based Dynamic Approach to Gaussian Mixture Modeling, IEEE Trans. on Systems, Man, and Cybernetics -- A, Vol. 29, No. 4, pp. 393 -- 399, July 1999

.... possible to employ the global k means algorithm as a method for providing e ective initial parameter values for RBF networks and data modeling problems using Gaussian mixture models and compare the e ectiveness of the obtained solutions with other training techniques for Gaussian mixture models [12, 13]. Acknowledgements N. Vlassis and J. J. Verbeek are supported by the Dutch Technology Foundation STW project AIF 4997. ....

N. Vlassis and A. Likas, \A kurtosis-based dynamic approach to Gaussian mixture modeling," IEEE Trans. Systems, Man, and Cybernetics, Part A, vol. 29, pp. 393-399, July 1999.

.... possible to employ the global k means algorithm as a method for providing e#ective initial parameter values for RBF networks and data modeling problems using Gaussian mixture models and compare the e#ectiveness of the obtained solutions with other training techniques for Gaussian mixture models [12, 13]. Acknowledgements N. Vlassis and J. J. Verbeek are supported by the Dutch Technology Foundation STW project AIF 4997. ....

N. Vlassis and A. Likas, "A kurtosis-based dynamic approach to Gaussian mixture modeling," IEEE Trans. Systems, Man, and Cybernetics, Part A, vol. 29, pp. 393--399, July 1999.

....EM a better (hopefully global) optimum is found. An important bene t of our new method over [12] is that the new algorithm produces a sequence of mixtures that can be used to perform model complexity selection as the mixtures are learned. For example the model selection criterion proposed in [13], which is based on kurtosis tests may be used here. In [6] it is proposed to start with a large number kmax of mixture components and to successively annihilate components with small mixing weights. This approach can be characterized as pruning a given mixture, where our approach can be ....

N. Vlassis and A. Likas. A kurtosis-based dynamic approach to Gaussian mixture modeling. IEEE Trans. Systems, Man, and Cybernetics, Part A, 29:393-399, 1999.

....peforms on average signi cantly better than the approach in [22] Both algorithms use roughly the same approach: the mixture is build up by starting with a one component mixture and adding new components one after the other. The new algorithm replaces the static component insertion step of [21] with a procedure that inserts a component that is selected among a set of candidate components dependent on the existing mixture. The paper is organized as follows: In Section 2 we recapitulate the de nition and EM learning of Gaussian mixtures. Section 3 forms the core of the paper and ....

....An important bene t of our new method over [19] is that the new algorithm produces a sequence of mixtures that can be used to perform model complexity selection as the mixtures are learned. For example a kurtosis based selection Section 5 Discussion and Conclusions 15 criterion, like the one in [21], can be used here. In [8] it is proposed to start with a large number k max of mixture components and to successively annihilate components with small mixing weights. This approach can be characterized as pruning a given mixture, where our approach can be characterized as growing a mixture. ....

N. Vlassis and A. Likas. A kurtosis-based dynamic approach to Gaussian mixture modeling. IEEE Trans. Systems, Man, and Cybernetics, Part A, 29:393-399, 1999.

....dynamically adjust the number of kernels. Specifying the number of basis functions is an important open research issue in RBF training and mixture modeling, and our aim is to check the adaptation and applicability of the several techniques proposed so far in the framework of the PRBF network [14] [15]. ACKNOWLEDGMENT The authors would like to thank the anonymous referees for their useful suggestions. ....

N. A. Vlassis and A. Likas, "A Kurtosis-based dynamic approach to Gaussian mixture modeling," IEEE Trans. Syst., Man. Cybern. A, vol. 29, pp. 393--399,

.... possible to employ the global k means algorithm as a method for providing e ective initial parameter values for RBF networks and data modeling problems using Gaussian mixture models and compare the e ectiveness of the obtained solutions with other training techniques for Gaussian mixture models [10, 11]. Acknowledgements N. Vlassis and J. J. Verbeek are supported by the Dutch Technology Foundation STW project AIF 4997. ....

N. Vlassis and A. Likas, \A kurtosis-based dynamic approach to Gaussian mixture modeling, " IEEE Trans. Systems, Man, and Cybernetics, Part A, vol. 29, no. 4, pp. 393-399,

....a component density and the empirical density in the vicinity of the component. In the past we have also proposed an incremental scheme for learning univariate Gaussian mixtures, in which a component of the mixture is split according to a statistical test involving the kurtosis of the component [18]. However, the proposed greedy EM algorithm seems to be more robust and avoids possible problems of the kurtosis related to outliers. Ongoing research focuses on two directions. First we are investigating the possibility of applying this technique in learning latent mixture models [6, 16] A ....

N. Vlassis and A. Likas. A kurtosis-based dynamic approach to Gaussian mixture modeling. IEEE Trans. Systems, Man, and Cybernetics, Part A, 29(4):393-399, July 1999.

....is the Kullback divergence between a component density and the empirical density (e.g. through kernel smoothing) in the vicinity of the component. 2 N. Vlassis However, the asymptotic distribution of this statistic is not known and the critical region of the test must be set heuristically. In [Vlassis and Likas, 1999] we proposed the use of kurtosis for deciding on the number of components in one dimensional mixture problems. In this paper we extend the approach to the multivariate case. The idea is, assuming k components, to apply EM steps until convergence and then add one more component to the mixture ....

....and real datasets. 2 The EM algorithm for k component Gaussian mixtures We rst describe brie y the EM algorithm for Gaussian mixtures with a xed number of components k. Details can be found in several textbooks, e.g. McLachlan and Krishnan, 1997] A brief description is also given in [Vlassis and Likas, 1999]. A multivariate Gaussian mixture is de ned as the weighted sum (1) with f(x; j ) the d dimensional Gaussian density f(x; j ) 2 ) d=2 jS j j 1=2 exp h 0:5(x m j ) T S 1 j (x m j ) i (3) parametrized on the mean m j and the covariance matrix S j , collectively denoted by the ....

[Article contains additional citation context not shown here]

N. Vlassis and A. Likas. A kurtosis-based dynamic approach to Gaussian mixture modeling. IEEE Trans. Systems, Man, and Cybernetics, Part A, 29(4):393-399, July 1999.

....a component density and the empirical density in the vicinity of the component. In the past we have also proposed an incremental scheme for learning univariate Gaussian mixtures, in which a component of the mixture is split according to a statistical test involving the kurtosis of the component [18]. However, the proposed greedy EM algorithm seems to be more robust and avoids possible problems of the kurtosis related to outliers. Ongoing research focuses on two directions. First we are investigating the possibility of applying this technique in learning latent mixture models [6, 16] A ....

N. Vlassis and A. Likas. A kurtosis-based dynamic approach to Gaussian mixture modeling. IEEE Trans. Systems, Man, and Cybernetics, Part A, 29(4):393-399, July 1999.

....Such known techniques are based on the likelihood ratio test [McLachlan, 1987] tests of homogeneity against mixture alternatives [Zelterman and Chen, 1988] or graphical techniques [Lindsay and Roeder, 1992] The extension of these methods to multivariate data is however not always easy. In [Vlassis and Likas, 1999] we proposed the use of kurtosis for deciding on the number of components in one dimensional mixture problems. In this paper we extend the approach to the multivariate case. The idea is, assuming k components, to apply EM steps until convergence and then add one more component to the mixture ....

....and real datasets. 2 The EM algorithm for k component Gaussian mixtures We rst describe brie y the EM algorithm for Gaussian mixtures with a xed number of components k. Details can be found in several textbooks, e.g. McLachlan and Krishnan, 1997] A brief description is also given in [Vlassis and Likas, 1999]. A multivariate Gaussian mixture is de ned as the weighted sum (1) with f(x; j ) the d dimensional Gaussian density f(x; j ) 2 ) d=2 jS j j 1=2 exp h 0:5(x m j ) T S 1 j (x m j ) i (3) parametrized on the mean m j and the covariance matrix S j , collectively denoted by the ....

[Article contains additional citation context not shown here]

N. Vlassis and A. Likas. A kurtosis-based dynamic approach to Gaussian mixture modeling. IEEE Trans. on Systems, Man, and Cybernetics, Part A, 29(4):393{ 399, July 1999.

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N. Vlassis and A. Likas. A kurtosis-based dynamic approach to gaussian mixture modeling. IEEE Trans. Systems, Man, and Cybernetics, Part A, 29:393--399, 1999.

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N. Vlassis and A. Likas, "A Kurtosis-based Dynamic Approach to Gaussian Mixture Modeling," IEEE Trans. Systems, Man, and Cybernetics, Part A, vol. 29, pp. 393--399, 1999.

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N. Vlassis and A. Likas. A kurtosis-based dynamic approach to gaussian mixture modeling. IEEE Trans. in Systems, Man and Cybernetics, 29(4):393 -- 399, 1999.

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